Title

Weak Galerkin methods for time-dependent Maxwell's equations

Document Type

Article

Publication Date

1-1-2017

Publication Title

Computers and Mathematics with Applications

Volume

74

Issue

9

First page number:

2106

Last page number:

2124

Abstract

This paper adapts the weak Galerkin (WG) finite element scheme to Maxwell's equations in the time domain. Developed by Wang and Ye in 2011, the WG scheme is a discontinuous Galerkin-like method that relies on a new notion of the discrete weak derivative. The WG method as applied to Maxwell's equations uses a discrete weak curl and an extra stabilization term to enforce a weak continuity of the solution across elements. Semi-discrete and fully-discrete schemes are developed and are shown to be unconditionally stable. An optimal order of convergence is proven in an appropriate energy norm and confirmed by numerical results. For clarity, the theoretical analysis is carried out for 3-D case. Some details showing how to implement this WG scheme in 2-D are provided and numerical results are given in 2-D. © 2017 Elsevier Ltd

Language

english

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